Quantum Fluctuations, Temperature, and Detuning Effects in Solid-Light Systems

Abstract

The superfluid to Mott insulator transition in cavity polariton arrays is analyzed using the variational cluster approach, taking into account quantum fluctuations exactly on finite length scales. Phase diagrams in one and two dimensions exhibit important non-mean-field features. Single-particle excitation spectra in the Mott phase are dominated by particle and hole bands separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows for changing the nature of the bosonic particles from quasilocalized excitons to polaritons to weakly interacting photons. The Mott state with density one exists up to temperatures T /g 0.03, implying experimentally accessible temperatures for realistic cavity couplings g. PACS numbers: 71.36.+c, 73.43.Nq, 78.20.Bh, 42.50.Ct The prospect of realizing a tunable, strongly correlated system of photons is exciting, both as a testbed for quantum many-body dynamics and for the potential of quantum simulators and other advanced quantum devices. Three proposals based on cavity-QED arrays have recently shown how this might be accomplished [1,2,3], followed by further work [4,5,6,7,8]. Engineered strong photon-photon interactions and hopping between cavities allow photons (as a component of cavity polaritons) to behave much like electrons or atoms in a many-body context. It is clear that a particular signature of quantum many-body physics, the superfluid (SF) to Mott insulator (MI) transition, should be reproducible in such systems and be similar to the widely studied Bose-Hubbard model (BHM). Yet, the BH analogy is not complete. The mixed matter-light nature of the system brings new physics yet to be fully explored."Solid-light" systems-so-named for the intriguing MI state of photons they exhibit-are reminiscent of cold atom optical lattices (CAOL) [9], but have some advantages concerning direct addressing of individual sites and device integration, and the potential for asymmetry construction by individual tuning, local variation, and far from equilibrium devices [4]. Photons as part of the system serve as excellent experimental probes, and have excellent "flying" potential so that they can be transported over long distances. Temporal and spatial correlation functions are accessible, and nonequilibrium quantum dynamics may be studied using coherent laser pumping to create initial states. Here ω 0 is the cavity photon energy, and ∆ = ω 0 − ǫ defines the detuning. Each cavity is described by the well-known Jaynes-Cummings (JC) HamiltonianĤ JC . The atom-photon coupling g (a † i , a i are photon creation and annihilation operators) gives rise to formation of polaritons (combined atomphoton excitations) whose numberN p = i (a † i a i +|↑ i ↑ i |) is conserved and couples to the chemical potential µ [7]. We consider nearest-neighbor photon hopping with amplitude t, define the polariton density n = N p /L, use g as the unit of energy and set ω 0 /g [23], k B and the lattice constant to one.Hamiltonian (1) represents a generic model of strongly correlated photons amenable to numer...

Excitation spectra of strongly correlated lattice bosons and polaritons

“…A number of authors have addressed the dynamics of the Bose-Hubbard model in different dimensions, 12,13,14,15,16,17,18,19,20,21,22,23 with results providing valuable information about the underlying physics, while corresponding work on coupled cavity models has just begun. 24,25 The two most important dynamic observables are the dynamic structure factor and the single-particle spectral function, which are also at the heart of theoretical and experimental works on Bose fluids. 26 Experimentally, the dynamic structure factor may be measured by Bragg spectroscopy or lattice modulation (in cold atomic gases) as well as by neutron scattering (in liquid helium), and single-particle excitations of optical solid-state systems are accessible by means of photoluminescence measurements.…”

Polaritonic properties of the Jaynes–Cummings lattice model in two dimensions

“…VCA has been previously applied to lightmatter systems in Refs. [15,16,30]. The main idea of VCA is that the self-energy Σ of the physical systemĤ JCL is approximated by the one of a so-called reference system H ′ , which shares its interaction part withĤ JCL and is exactly solvable.…”

“…The two-dimensional JCL model exhibits a quantum phase transition from the Mott phase, where polaritons are localized within the cavities, to the superfluid phase, where polaritons delocalize on the whole lattice [5,15,17,18]. We evaluate the phase boundary for zero detuning ∆ = 0 by means of VCA from the minimal excitation energies of the system, see Fig.…”

“…Most of the work has been devoted to study its ground state properties. The quantum phase transition from the Mott to the superfluid phase has been investigated by means of density matrix renormalization group [13,14], the variational cluster approach [15,16], quantum Monte Carlo (QMC) [17], and analytically by means of strong coupling perturbation theory [18,19]. Results are also available on mean field level [5,20]; some signatures of the quantum phase transition have also been determined from exact diagonalization of small systems consisting of a few cavities [6,21,22].…”

Quantum-state transfer in staggered coupled-cavity arrays

“…In the strong atom-field coupling regime, an effective repulsive photon-photon interaction takes place, resulting in a Mott-insulator state for the system [3][4][5][6][7][8][9][10][11][12]. The competition between this photon-blockade effect [13] and the photon hopping creates a Mott-insulator-superfluid quantum phase transition in analogy with the Bose-Hubbard model [14].…”